(CNN) -- A Texas state board said Friday that arson investigators used flawed science but were not negligent in an investigation that led to a controversial 2004 execution.

The panel also said that investigators did not commit misconduct.

Cameron Todd Willingham was executed in 2004, 13 years after a fire killed his three daughters. Prosecutors argued that Willingham deliberately set the 1991 blaze -- but three reviews of the evidence by outside experts have found the fire should not have been ruled arson.

The last of those reports was ordered by the Texas Forensic Science Commission, which has been looking into Willingham's execution since 2008. A September 2009 shake-up by Texas Gov. Rick Perry kept that panel from reviewing the report.

But on Friday, the panel declared that investigators were using the science available to them at the time, even though it was flawed. The board said it would present its final report for a vote at a meeting in October.

The Forensic Science Commission's chairman is now John Bradley, an Austin-area district attorney with a reputation as a staunch supporter of the death penalty. Bradley has pledged to state lawmakers that the Willingham investigation "absolutely" will continue -- but said the panel needs better rules to guide its work, and could not say when the Willingham issue would move forward.

Thursday, he told CNN that the concerns of Willingham's supporters are based on "a lot of misinformation."

"I think that's being used very much as a side issue to politicize, through some New York lawyers, the work of the commission," Bradley said. "The commission has been very clear that the commission is going to address the merits of the Willingham case."

The panel also said Friday that a legal opinion that challenged the panel's jurisdiction in the matter was not the "law" of the commission, state Sen. Rodney Ellis said.

On Friday, he said he was "happy" to hear the investigation would continue, but concerned that the investigation was looking for misconduct and negligence in the wrong place.

"Unfortunately, the commission is off-track in terms of what it should be investigating," he said in a statement. "It was painfully apparent that many FSC members believe that flawed science was used in the Willingham conviction, but the FSC does not seem interested in looking at the bigger picture: When did the State Fire Marshal start using modern arson science and did the State Fire Marshal commit professional negligence or misconduct when it failed to inform the courts, prosecutors, the Board of Pardons and Parole, and the Governor that flawed arson science had been used to convict hundreds of defendants?"

Ellis, a Houston Democrat, serves as the chairman of the board of The Innocence Project -- the "New York lawyers" that have supported efforts by Willingham's stepmother and cousins to clear his name. The group advocates for prisoners it says are wrongly convicted, and Ellis said the commission's work "is too important to be bogged down in political bickering."

"Texans need the FSC to perform its work in a timely manner, so the public can once again have confidence in forensic evidence and confidence that the truly guilty are behind bars and the innocent are free," he said.

But Bradley said the commission has never decided to apply the logic of the legal opinion to the case on Friday's agenda.

Bradley was named the panel's chairman two days before the Forensic Science Commission was to hear from Craig Beyler, a Maryland-based fire science expert. Beyler concluded the arson finding at the heart of the Willingham case "could not be sustained," either by current standards or those in place at the time.

The Innocence Project requested the investigation after a report it commissioned reached the same conclusion. Death-penalty opponents say an impartial review of Willingham's case could lead to the unprecedented admission that the state executed an innocent man.

Perry, who signed off on Willingham's execution, is up for re-election in November, and his critics have accused him of trying to short-circuit the review. Perry has said he remains confident of the condemned man's guilt, and police in the town of Corsicana, where the fire occurred, say other evidence beyond the arson testimony Beyler criticized supports the prosecution.

Cox, a retired nurse in Ardmore, Oklahoma, told CNN that spiking the commission's investigation would be a "blatant miscarriage of justice."

"The reasonable people of this country and the state of Texas can see through what this is," she said.